Girish Mahajan (Editor)

Euler integral

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In mathematics, there are two types of Euler integral:

1. Euler integral of the first kind: the Beta function B ( x , y ) = ∫ 0 1 t x − 1 ( 1 − t ) y − 1 d t = Γ ( x ) Γ ( y ) Γ ( x + y ) 2. Euler integral of the second kind: the Gamma function Γ ( z ) = ∫ 0 ∞ t z − 1 e − t d t

For positive integers m and n

B ( n , m ) = ( n − 1 ) ! ( m − 1 ) ! ( n + m − 1 ) ! = n + m n m ( n + m n ) Γ ( n ) = ( n − 1 ) !

References

Euler integral Wikipedia
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